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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math.stat.descriptive.moment;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math.exception.NullArgumentException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math.exception.util.LocalizedFormats;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math.stat.descriptive.WeightedEvaluation;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    /**<a name="line.26"></a>
<FONT color="green">027</FONT>     * Computes the variance of the available values.  By default, the unbiased<a name="line.27"></a>
<FONT color="green">028</FONT>     * "sample variance" definitional formula is used:<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;p&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * variance = sum((x_i - mean)^2) / (n - 1) &lt;/p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * where mean is the {@link Mean} and &lt;code&gt;n&lt;/code&gt; is the number<a name="line.32"></a>
<FONT color="green">033</FONT>     * of sample observations.&lt;/p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     * &lt;p&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>     * The definitional formula does not have good numerical properties, so<a name="line.35"></a>
<FONT color="green">036</FONT>     * this implementation does not compute the statistic using the definitional<a name="line.36"></a>
<FONT color="green">037</FONT>     * formula. &lt;ul&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     * &lt;li&gt; The &lt;code&gt;getResult&lt;/code&gt; method computes the variance using<a name="line.38"></a>
<FONT color="green">039</FONT>     * updating formulas based on West's algorithm, as described in<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;a href="http://doi.acm.org/10.1145/359146.359152"&gt; Chan, T. F. and<a name="line.40"></a>
<FONT color="green">041</FONT>     * J. G. Lewis 1979, &lt;i&gt;Communications of the ACM&lt;/i&gt;,<a name="line.41"></a>
<FONT color="green">042</FONT>     * vol. 22 no. 9, pp. 526-531.&lt;/a&gt;&lt;/li&gt;<a name="line.42"></a>
<FONT color="green">043</FONT>     * &lt;li&gt; The &lt;code&gt;evaluate&lt;/code&gt; methods leverage the fact that they have the<a name="line.43"></a>
<FONT color="green">044</FONT>     * full array of values in memory to execute a two-pass algorithm.<a name="line.44"></a>
<FONT color="green">045</FONT>     * Specifically, these methods use the "corrected two-pass algorithm" from<a name="line.45"></a>
<FONT color="green">046</FONT>     * Chan, Golub, Levesque, &lt;i&gt;Algorithms for Computing the Sample Variance&lt;/i&gt;,<a name="line.46"></a>
<FONT color="green">047</FONT>     * American Statistician, vol. 37, no. 3 (1983) pp. 242-247.&lt;/li&gt;&lt;/ul&gt;<a name="line.47"></a>
<FONT color="green">048</FONT>     * Note that adding values using &lt;code&gt;increment&lt;/code&gt; or<a name="line.48"></a>
<FONT color="green">049</FONT>     * &lt;code&gt;incrementAll&lt;/code&gt; and then executing &lt;code&gt;getResult&lt;/code&gt; will<a name="line.49"></a>
<FONT color="green">050</FONT>     * sometimes give a different, less accurate, result than executing<a name="line.50"></a>
<FONT color="green">051</FONT>     * &lt;code&gt;evaluate&lt;/code&gt; with the full array of values. The former approach<a name="line.51"></a>
<FONT color="green">052</FONT>     * should only be used when the full array of values is not available.&lt;/p&gt;<a name="line.52"></a>
<FONT color="green">053</FONT>     * &lt;p&gt;<a name="line.53"></a>
<FONT color="green">054</FONT>     * The "population variance"  ( sum((x_i - mean)^2) / n ) can also<a name="line.54"></a>
<FONT color="green">055</FONT>     * be computed using this statistic.  The &lt;code&gt;isBiasCorrected&lt;/code&gt;<a name="line.55"></a>
<FONT color="green">056</FONT>     * property determines whether the "population" or "sample" value is<a name="line.56"></a>
<FONT color="green">057</FONT>     * returned by the &lt;code&gt;evaluate&lt;/code&gt; and &lt;code&gt;getResult&lt;/code&gt; methods.<a name="line.57"></a>
<FONT color="green">058</FONT>     * To compute population variances, set this property to &lt;code&gt;false.&lt;/code&gt;<a name="line.58"></a>
<FONT color="green">059</FONT>     * &lt;/p&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>     * &lt;p&gt;<a name="line.60"></a>
<FONT color="green">061</FONT>     * &lt;strong&gt;Note that this implementation is not synchronized.&lt;/strong&gt; If<a name="line.61"></a>
<FONT color="green">062</FONT>     * multiple threads access an instance of this class concurrently, and at least<a name="line.62"></a>
<FONT color="green">063</FONT>     * one of the threads invokes the &lt;code&gt;increment()&lt;/code&gt; or<a name="line.63"></a>
<FONT color="green">064</FONT>     * &lt;code&gt;clear()&lt;/code&gt; method, it must be synchronized externally.&lt;/p&gt;<a name="line.64"></a>
<FONT color="green">065</FONT>     *<a name="line.65"></a>
<FONT color="green">066</FONT>     * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $<a name="line.66"></a>
<FONT color="green">067</FONT>     */<a name="line.67"></a>
<FONT color="green">068</FONT>    public class Variance extends AbstractStorelessUnivariateStatistic implements Serializable, WeightedEvaluation {<a name="line.68"></a>
<FONT color="green">069</FONT>    <a name="line.69"></a>
<FONT color="green">070</FONT>        /** Serializable version identifier */<a name="line.70"></a>
<FONT color="green">071</FONT>        private static final long serialVersionUID = -9111962718267217978L;<a name="line.71"></a>
<FONT color="green">072</FONT>    <a name="line.72"></a>
<FONT color="green">073</FONT>        /** SecondMoment is used in incremental calculation of Variance*/<a name="line.73"></a>
<FONT color="green">074</FONT>        protected SecondMoment moment = null;<a name="line.74"></a>
<FONT color="green">075</FONT>    <a name="line.75"></a>
<FONT color="green">076</FONT>        /**<a name="line.76"></a>
<FONT color="green">077</FONT>         * Boolean test to determine if this Variance should also increment<a name="line.77"></a>
<FONT color="green">078</FONT>         * the second moment, this evaluates to false when this Variance is<a name="line.78"></a>
<FONT color="green">079</FONT>         * constructed with an external SecondMoment as a parameter.<a name="line.79"></a>
<FONT color="green">080</FONT>         */<a name="line.80"></a>
<FONT color="green">081</FONT>        protected boolean incMoment = true;<a name="line.81"></a>
<FONT color="green">082</FONT>    <a name="line.82"></a>
<FONT color="green">083</FONT>        /**<a name="line.83"></a>
<FONT color="green">084</FONT>         * Determines whether or not bias correction is applied when computing the<a name="line.84"></a>
<FONT color="green">085</FONT>         * value of the statisic.  True means that bias is corrected.  See<a name="line.85"></a>
<FONT color="green">086</FONT>         * {@link Variance} for details on the formula.<a name="line.86"></a>
<FONT color="green">087</FONT>         */<a name="line.87"></a>
<FONT color="green">088</FONT>        private boolean isBiasCorrected = true;<a name="line.88"></a>
<FONT color="green">089</FONT>    <a name="line.89"></a>
<FONT color="green">090</FONT>        /**<a name="line.90"></a>
<FONT color="green">091</FONT>         * Constructs a Variance with default (true) &lt;code&gt;isBiasCorrected&lt;/code&gt;<a name="line.91"></a>
<FONT color="green">092</FONT>         * property.<a name="line.92"></a>
<FONT color="green">093</FONT>         */<a name="line.93"></a>
<FONT color="green">094</FONT>        public Variance() {<a name="line.94"></a>
<FONT color="green">095</FONT>            moment = new SecondMoment();<a name="line.95"></a>
<FONT color="green">096</FONT>        }<a name="line.96"></a>
<FONT color="green">097</FONT>    <a name="line.97"></a>
<FONT color="green">098</FONT>        /**<a name="line.98"></a>
<FONT color="green">099</FONT>         * Constructs a Variance based on an external second moment.<a name="line.99"></a>
<FONT color="green">100</FONT>         *<a name="line.100"></a>
<FONT color="green">101</FONT>         * @param m2 the SecondMoment (Third or Fourth moments work<a name="line.101"></a>
<FONT color="green">102</FONT>         * here as well.)<a name="line.102"></a>
<FONT color="green">103</FONT>         */<a name="line.103"></a>
<FONT color="green">104</FONT>        public Variance(final SecondMoment m2) {<a name="line.104"></a>
<FONT color="green">105</FONT>            incMoment = false;<a name="line.105"></a>
<FONT color="green">106</FONT>            this.moment = m2;<a name="line.106"></a>
<FONT color="green">107</FONT>        }<a name="line.107"></a>
<FONT color="green">108</FONT>    <a name="line.108"></a>
<FONT color="green">109</FONT>        /**<a name="line.109"></a>
<FONT color="green">110</FONT>         * Constructs a Variance with the specified &lt;code&gt;isBiasCorrected&lt;/code&gt;<a name="line.110"></a>
<FONT color="green">111</FONT>         * property<a name="line.111"></a>
<FONT color="green">112</FONT>         *<a name="line.112"></a>
<FONT color="green">113</FONT>         * @param isBiasCorrected  setting for bias correction - true means<a name="line.113"></a>
<FONT color="green">114</FONT>         * bias will be corrected and is equivalent to using the argumentless<a name="line.114"></a>
<FONT color="green">115</FONT>         * constructor<a name="line.115"></a>
<FONT color="green">116</FONT>         */<a name="line.116"></a>
<FONT color="green">117</FONT>        public Variance(boolean isBiasCorrected) {<a name="line.117"></a>
<FONT color="green">118</FONT>            moment = new SecondMoment();<a name="line.118"></a>
<FONT color="green">119</FONT>            this.isBiasCorrected = isBiasCorrected;<a name="line.119"></a>
<FONT color="green">120</FONT>        }<a name="line.120"></a>
<FONT color="green">121</FONT>    <a name="line.121"></a>
<FONT color="green">122</FONT>        /**<a name="line.122"></a>
<FONT color="green">123</FONT>         * Constructs a Variance with the specified &lt;code&gt;isBiasCorrected&lt;/code&gt;<a name="line.123"></a>
<FONT color="green">124</FONT>         * property and the supplied external second moment.<a name="line.124"></a>
<FONT color="green">125</FONT>         *<a name="line.125"></a>
<FONT color="green">126</FONT>         * @param isBiasCorrected  setting for bias correction - true means<a name="line.126"></a>
<FONT color="green">127</FONT>         * bias will be corrected<a name="line.127"></a>
<FONT color="green">128</FONT>         * @param m2 the SecondMoment (Third or Fourth moments work<a name="line.128"></a>
<FONT color="green">129</FONT>         * here as well.)<a name="line.129"></a>
<FONT color="green">130</FONT>         */<a name="line.130"></a>
<FONT color="green">131</FONT>        public Variance(boolean isBiasCorrected, SecondMoment m2) {<a name="line.131"></a>
<FONT color="green">132</FONT>            incMoment = false;<a name="line.132"></a>
<FONT color="green">133</FONT>            this.moment = m2;<a name="line.133"></a>
<FONT color="green">134</FONT>            this.isBiasCorrected = isBiasCorrected;<a name="line.134"></a>
<FONT color="green">135</FONT>        }<a name="line.135"></a>
<FONT color="green">136</FONT>    <a name="line.136"></a>
<FONT color="green">137</FONT>        /**<a name="line.137"></a>
<FONT color="green">138</FONT>         * Copy constructor, creates a new {@code Variance} identical<a name="line.138"></a>
<FONT color="green">139</FONT>         * to the {@code original}<a name="line.139"></a>
<FONT color="green">140</FONT>         *<a name="line.140"></a>
<FONT color="green">141</FONT>         * @param original the {@code Variance} instance to copy<a name="line.141"></a>
<FONT color="green">142</FONT>         */<a name="line.142"></a>
<FONT color="green">143</FONT>        public Variance(Variance original) {<a name="line.143"></a>
<FONT color="green">144</FONT>            copy(original, this);<a name="line.144"></a>
<FONT color="green">145</FONT>        }<a name="line.145"></a>
<FONT color="green">146</FONT>    <a name="line.146"></a>
<FONT color="green">147</FONT>        /**<a name="line.147"></a>
<FONT color="green">148</FONT>         * {@inheritDoc}<a name="line.148"></a>
<FONT color="green">149</FONT>         * &lt;p&gt;If all values are available, it is more accurate to use<a name="line.149"></a>
<FONT color="green">150</FONT>         * {@link #evaluate(double[])} rather than adding values one at a time<a name="line.150"></a>
<FONT color="green">151</FONT>         * using this method and then executing {@link #getResult}, since<a name="line.151"></a>
<FONT color="green">152</FONT>         * &lt;code&gt;evaluate&lt;/code&gt; leverages the fact that is has the full<a name="line.152"></a>
<FONT color="green">153</FONT>         * list of values together to execute a two-pass algorithm.<a name="line.153"></a>
<FONT color="green">154</FONT>         * See {@link Variance}.&lt;/p&gt;<a name="line.154"></a>
<FONT color="green">155</FONT>         */<a name="line.155"></a>
<FONT color="green">156</FONT>        @Override<a name="line.156"></a>
<FONT color="green">157</FONT>        public void increment(final double d) {<a name="line.157"></a>
<FONT color="green">158</FONT>            if (incMoment) {<a name="line.158"></a>
<FONT color="green">159</FONT>                moment.increment(d);<a name="line.159"></a>
<FONT color="green">160</FONT>            }<a name="line.160"></a>
<FONT color="green">161</FONT>        }<a name="line.161"></a>
<FONT color="green">162</FONT>    <a name="line.162"></a>
<FONT color="green">163</FONT>        /**<a name="line.163"></a>
<FONT color="green">164</FONT>         * {@inheritDoc}<a name="line.164"></a>
<FONT color="green">165</FONT>         */<a name="line.165"></a>
<FONT color="green">166</FONT>        @Override<a name="line.166"></a>
<FONT color="green">167</FONT>        public double getResult() {<a name="line.167"></a>
<FONT color="green">168</FONT>                if (moment.n == 0) {<a name="line.168"></a>
<FONT color="green">169</FONT>                    return Double.NaN;<a name="line.169"></a>
<FONT color="green">170</FONT>                } else if (moment.n == 1) {<a name="line.170"></a>
<FONT color="green">171</FONT>                    return 0d;<a name="line.171"></a>
<FONT color="green">172</FONT>                } else {<a name="line.172"></a>
<FONT color="green">173</FONT>                    if (isBiasCorrected) {<a name="line.173"></a>
<FONT color="green">174</FONT>                        return moment.m2 / (moment.n - 1d);<a name="line.174"></a>
<FONT color="green">175</FONT>                    } else {<a name="line.175"></a>
<FONT color="green">176</FONT>                        return moment.m2 / (moment.n);<a name="line.176"></a>
<FONT color="green">177</FONT>                    }<a name="line.177"></a>
<FONT color="green">178</FONT>                }<a name="line.178"></a>
<FONT color="green">179</FONT>        }<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>        /**<a name="line.181"></a>
<FONT color="green">182</FONT>         * {@inheritDoc}<a name="line.182"></a>
<FONT color="green">183</FONT>         */<a name="line.183"></a>
<FONT color="green">184</FONT>        public long getN() {<a name="line.184"></a>
<FONT color="green">185</FONT>            return moment.getN();<a name="line.185"></a>
<FONT color="green">186</FONT>        }<a name="line.186"></a>
<FONT color="green">187</FONT>    <a name="line.187"></a>
<FONT color="green">188</FONT>        /**<a name="line.188"></a>
<FONT color="green">189</FONT>         * {@inheritDoc}<a name="line.189"></a>
<FONT color="green">190</FONT>         */<a name="line.190"></a>
<FONT color="green">191</FONT>        @Override<a name="line.191"></a>
<FONT color="green">192</FONT>        public void clear() {<a name="line.192"></a>
<FONT color="green">193</FONT>            if (incMoment) {<a name="line.193"></a>
<FONT color="green">194</FONT>                moment.clear();<a name="line.194"></a>
<FONT color="green">195</FONT>            }<a name="line.195"></a>
<FONT color="green">196</FONT>        }<a name="line.196"></a>
<FONT color="green">197</FONT>    <a name="line.197"></a>
<FONT color="green">198</FONT>        /**<a name="line.198"></a>
<FONT color="green">199</FONT>         * Returns the variance of the entries in the input array, or<a name="line.199"></a>
<FONT color="green">200</FONT>         * &lt;code&gt;Double.NaN&lt;/code&gt; if the array is empty.<a name="line.200"></a>
<FONT color="green">201</FONT>         * &lt;p&gt;<a name="line.201"></a>
<FONT color="green">202</FONT>         * See {@link Variance} for details on the computing algorithm.&lt;/p&gt;<a name="line.202"></a>
<FONT color="green">203</FONT>         * &lt;p&gt;<a name="line.203"></a>
<FONT color="green">204</FONT>         * Returns 0 for a single-value (i.e. length = 1) sample.&lt;/p&gt;<a name="line.204"></a>
<FONT color="green">205</FONT>         * &lt;p&gt;<a name="line.205"></a>
<FONT color="green">206</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if the array is null.&lt;/p&gt;<a name="line.206"></a>
<FONT color="green">207</FONT>         * &lt;p&gt;<a name="line.207"></a>
<FONT color="green">208</FONT>         * Does not change the internal state of the statistic.&lt;/p&gt;<a name="line.208"></a>
<FONT color="green">209</FONT>         *<a name="line.209"></a>
<FONT color="green">210</FONT>         * @param values the input array<a name="line.210"></a>
<FONT color="green">211</FONT>         * @return the variance of the values or Double.NaN if length = 0<a name="line.211"></a>
<FONT color="green">212</FONT>         * @throws IllegalArgumentException if the array is null<a name="line.212"></a>
<FONT color="green">213</FONT>         */<a name="line.213"></a>
<FONT color="green">214</FONT>        @Override<a name="line.214"></a>
<FONT color="green">215</FONT>        public double evaluate(final double[] values) {<a name="line.215"></a>
<FONT color="green">216</FONT>            if (values == null) {<a name="line.216"></a>
<FONT color="green">217</FONT>                throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);<a name="line.217"></a>
<FONT color="green">218</FONT>            }<a name="line.218"></a>
<FONT color="green">219</FONT>            return evaluate(values, 0, values.length);<a name="line.219"></a>
<FONT color="green">220</FONT>        }<a name="line.220"></a>
<FONT color="green">221</FONT>    <a name="line.221"></a>
<FONT color="green">222</FONT>        /**<a name="line.222"></a>
<FONT color="green">223</FONT>         * Returns the variance of the entries in the specified portion of<a name="line.223"></a>
<FONT color="green">224</FONT>         * the input array, or &lt;code&gt;Double.NaN&lt;/code&gt; if the designated subarray<a name="line.224"></a>
<FONT color="green">225</FONT>         * is empty.<a name="line.225"></a>
<FONT color="green">226</FONT>         * &lt;p&gt;<a name="line.226"></a>
<FONT color="green">227</FONT>         * See {@link Variance} for details on the computing algorithm.&lt;/p&gt;<a name="line.227"></a>
<FONT color="green">228</FONT>         * &lt;p&gt;<a name="line.228"></a>
<FONT color="green">229</FONT>         * Returns 0 for a single-value (i.e. length = 1) sample.&lt;/p&gt;<a name="line.229"></a>
<FONT color="green">230</FONT>         * &lt;p&gt;<a name="line.230"></a>
<FONT color="green">231</FONT>         * Does not change the internal state of the statistic.&lt;/p&gt;<a name="line.231"></a>
<FONT color="green">232</FONT>         * &lt;p&gt;<a name="line.232"></a>
<FONT color="green">233</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if the array is null.&lt;/p&gt;<a name="line.233"></a>
<FONT color="green">234</FONT>         *<a name="line.234"></a>
<FONT color="green">235</FONT>         * @param values the input array<a name="line.235"></a>
<FONT color="green">236</FONT>         * @param begin index of the first array element to include<a name="line.236"></a>
<FONT color="green">237</FONT>         * @param length the number of elements to include<a name="line.237"></a>
<FONT color="green">238</FONT>         * @return the variance of the values or Double.NaN if length = 0<a name="line.238"></a>
<FONT color="green">239</FONT>         * @throws IllegalArgumentException if the array is null or the array index<a name="line.239"></a>
<FONT color="green">240</FONT>         *  parameters are not valid<a name="line.240"></a>
<FONT color="green">241</FONT>         */<a name="line.241"></a>
<FONT color="green">242</FONT>        @Override<a name="line.242"></a>
<FONT color="green">243</FONT>        public double evaluate(final double[] values, final int begin, final int length) {<a name="line.243"></a>
<FONT color="green">244</FONT>    <a name="line.244"></a>
<FONT color="green">245</FONT>            double var = Double.NaN;<a name="line.245"></a>
<FONT color="green">246</FONT>    <a name="line.246"></a>
<FONT color="green">247</FONT>            if (test(values, begin, length)) {<a name="line.247"></a>
<FONT color="green">248</FONT>                clear();<a name="line.248"></a>
<FONT color="green">249</FONT>                if (length == 1) {<a name="line.249"></a>
<FONT color="green">250</FONT>                    var = 0.0;<a name="line.250"></a>
<FONT color="green">251</FONT>                } else if (length &gt; 1) {<a name="line.251"></a>
<FONT color="green">252</FONT>                    Mean mean = new Mean();<a name="line.252"></a>
<FONT color="green">253</FONT>                    double m = mean.evaluate(values, begin, length);<a name="line.253"></a>
<FONT color="green">254</FONT>                    var = evaluate(values, m, begin, length);<a name="line.254"></a>
<FONT color="green">255</FONT>                }<a name="line.255"></a>
<FONT color="green">256</FONT>            }<a name="line.256"></a>
<FONT color="green">257</FONT>            return var;<a name="line.257"></a>
<FONT color="green">258</FONT>        }<a name="line.258"></a>
<FONT color="green">259</FONT>    <a name="line.259"></a>
<FONT color="green">260</FONT>        /**<a name="line.260"></a>
<FONT color="green">261</FONT>         * &lt;p&gt;Returns the weighted variance of the entries in the specified portion of<a name="line.261"></a>
<FONT color="green">262</FONT>         * the input array, or &lt;code&gt;Double.NaN&lt;/code&gt; if the designated subarray<a name="line.262"></a>
<FONT color="green">263</FONT>         * is empty.&lt;/p&gt;<a name="line.263"></a>
<FONT color="green">264</FONT>         * &lt;p&gt;<a name="line.264"></a>
<FONT color="green">265</FONT>         * Uses the formula &lt;pre&gt;<a name="line.265"></a>
<FONT color="green">266</FONT>         *   &amp;Sigma;(weights[i]*(values[i] - weightedMean)&lt;sup&gt;2&lt;/sup&gt;)/(&amp;Sigma;(weights[i]) - 1)<a name="line.266"></a>
<FONT color="green">267</FONT>         * &lt;/pre&gt;<a name="line.267"></a>
<FONT color="green">268</FONT>         * where weightedMean is the weighted mean&lt;/p&gt;<a name="line.268"></a>
<FONT color="green">269</FONT>         * &lt;p&gt;<a name="line.269"></a>
<FONT color="green">270</FONT>         * This formula will not return the same result as the unweighted variance when all<a name="line.270"></a>
<FONT color="green">271</FONT>         * weights are equal, unless all weights are equal to 1. The formula assumes that<a name="line.271"></a>
<FONT color="green">272</FONT>         * weights are to be treated as "expansion values," as will be the case if for example<a name="line.272"></a>
<FONT color="green">273</FONT>         * the weights represent frequency counts. To normalize weights so that the denominator<a name="line.273"></a>
<FONT color="green">274</FONT>         * in the variance computation equals the length of the input vector minus one, use &lt;pre&gt;<a name="line.274"></a>
<FONT color="green">275</FONT>         *   &lt;code&gt;evaluate(values, MathUtils.normalizeArray(weights, values.length)); &lt;/code&gt;<a name="line.275"></a>
<FONT color="green">276</FONT>         * &lt;/pre&gt;<a name="line.276"></a>
<FONT color="green">277</FONT>         * &lt;p&gt;<a name="line.277"></a>
<FONT color="green">278</FONT>         * Returns 0 for a single-value (i.e. length = 1) sample.&lt;/p&gt;<a name="line.278"></a>
<FONT color="green">279</FONT>         * &lt;p&gt;<a name="line.279"></a>
<FONT color="green">280</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if any of the following are true:<a name="line.280"></a>
<FONT color="green">281</FONT>         * &lt;ul&gt;&lt;li&gt;the values array is null&lt;/li&gt;<a name="line.281"></a>
<FONT color="green">282</FONT>         *     &lt;li&gt;the weights array is null&lt;/li&gt;<a name="line.282"></a>
<FONT color="green">283</FONT>         *     &lt;li&gt;the weights array does not have the same length as the values array&lt;/li&gt;<a name="line.283"></a>
<FONT color="green">284</FONT>         *     &lt;li&gt;the weights array contains one or more infinite values&lt;/li&gt;<a name="line.284"></a>
<FONT color="green">285</FONT>         *     &lt;li&gt;the weights array contains one or more NaN values&lt;/li&gt;<a name="line.285"></a>
<FONT color="green">286</FONT>         *     &lt;li&gt;the weights array contains negative values&lt;/li&gt;<a name="line.286"></a>
<FONT color="green">287</FONT>         *     &lt;li&gt;the start and length arguments do not determine a valid array&lt;/li&gt;<a name="line.287"></a>
<FONT color="green">288</FONT>         * &lt;/ul&gt;&lt;/p&gt;<a name="line.288"></a>
<FONT color="green">289</FONT>         * &lt;p&gt;<a name="line.289"></a>
<FONT color="green">290</FONT>         * Does not change the internal state of the statistic.&lt;/p&gt;<a name="line.290"></a>
<FONT color="green">291</FONT>         * &lt;p&gt;<a name="line.291"></a>
<FONT color="green">292</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if either array is null.&lt;/p&gt;<a name="line.292"></a>
<FONT color="green">293</FONT>         *<a name="line.293"></a>
<FONT color="green">294</FONT>         * @param values the input array<a name="line.294"></a>
<FONT color="green">295</FONT>         * @param weights the weights array<a name="line.295"></a>
<FONT color="green">296</FONT>         * @param begin index of the first array element to include<a name="line.296"></a>
<FONT color="green">297</FONT>         * @param length the number of elements to include<a name="line.297"></a>
<FONT color="green">298</FONT>         * @return the weighted variance of the values or Double.NaN if length = 0<a name="line.298"></a>
<FONT color="green">299</FONT>         * @throws IllegalArgumentException if the parameters are not valid<a name="line.299"></a>
<FONT color="green">300</FONT>         * @since 2.1<a name="line.300"></a>
<FONT color="green">301</FONT>         */<a name="line.301"></a>
<FONT color="green">302</FONT>        public double evaluate(final double[] values, final double[] weights,<a name="line.302"></a>
<FONT color="green">303</FONT>                               final int begin, final int length) {<a name="line.303"></a>
<FONT color="green">304</FONT>    <a name="line.304"></a>
<FONT color="green">305</FONT>            double var = Double.NaN;<a name="line.305"></a>
<FONT color="green">306</FONT>    <a name="line.306"></a>
<FONT color="green">307</FONT>            if (test(values, weights,begin, length)) {<a name="line.307"></a>
<FONT color="green">308</FONT>                clear();<a name="line.308"></a>
<FONT color="green">309</FONT>                if (length == 1) {<a name="line.309"></a>
<FONT color="green">310</FONT>                    var = 0.0;<a name="line.310"></a>
<FONT color="green">311</FONT>                } else if (length &gt; 1) {<a name="line.311"></a>
<FONT color="green">312</FONT>                    Mean mean = new Mean();<a name="line.312"></a>
<FONT color="green">313</FONT>                    double m = mean.evaluate(values, weights, begin, length);<a name="line.313"></a>
<FONT color="green">314</FONT>                    var = evaluate(values, weights, m, begin, length);<a name="line.314"></a>
<FONT color="green">315</FONT>                }<a name="line.315"></a>
<FONT color="green">316</FONT>            }<a name="line.316"></a>
<FONT color="green">317</FONT>            return var;<a name="line.317"></a>
<FONT color="green">318</FONT>        }<a name="line.318"></a>
<FONT color="green">319</FONT>    <a name="line.319"></a>
<FONT color="green">320</FONT>        /**<a name="line.320"></a>
<FONT color="green">321</FONT>         * &lt;p&gt;<a name="line.321"></a>
<FONT color="green">322</FONT>         * Returns the weighted variance of the entries in the the input array.&lt;/p&gt;<a name="line.322"></a>
<FONT color="green">323</FONT>         * &lt;p&gt;<a name="line.323"></a>
<FONT color="green">324</FONT>         * Uses the formula &lt;pre&gt;<a name="line.324"></a>
<FONT color="green">325</FONT>         *   &amp;Sigma;(weights[i]*(values[i] - weightedMean)&lt;sup&gt;2&lt;/sup&gt;)/(&amp;Sigma;(weights[i]) - 1)<a name="line.325"></a>
<FONT color="green">326</FONT>         * &lt;/pre&gt;<a name="line.326"></a>
<FONT color="green">327</FONT>         * where weightedMean is the weighted mean&lt;/p&gt;<a name="line.327"></a>
<FONT color="green">328</FONT>         * &lt;p&gt;<a name="line.328"></a>
<FONT color="green">329</FONT>         * This formula will not return the same result as the unweighted variance when all<a name="line.329"></a>
<FONT color="green">330</FONT>         * weights are equal, unless all weights are equal to 1. The formula assumes that<a name="line.330"></a>
<FONT color="green">331</FONT>         * weights are to be treated as "expansion values," as will be the case if for example<a name="line.331"></a>
<FONT color="green">332</FONT>         * the weights represent frequency counts. To normalize weights so that the denominator<a name="line.332"></a>
<FONT color="green">333</FONT>         * in the variance computation equals the length of the input vector minus one, use &lt;pre&gt;<a name="line.333"></a>
<FONT color="green">334</FONT>         *   &lt;code&gt;evaluate(values, MathUtils.normalizeArray(weights, values.length)); &lt;/code&gt;<a name="line.334"></a>
<FONT color="green">335</FONT>         * &lt;/pre&gt;<a name="line.335"></a>
<FONT color="green">336</FONT>         * &lt;p&gt;<a name="line.336"></a>
<FONT color="green">337</FONT>         * Returns 0 for a single-value (i.e. length = 1) sample.&lt;/p&gt;<a name="line.337"></a>
<FONT color="green">338</FONT>         * &lt;p&gt;<a name="line.338"></a>
<FONT color="green">339</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if any of the following are true:<a name="line.339"></a>
<FONT color="green">340</FONT>         * &lt;ul&gt;&lt;li&gt;the values array is null&lt;/li&gt;<a name="line.340"></a>
<FONT color="green">341</FONT>         *     &lt;li&gt;the weights array is null&lt;/li&gt;<a name="line.341"></a>
<FONT color="green">342</FONT>         *     &lt;li&gt;the weights array does not have the same length as the values array&lt;/li&gt;<a name="line.342"></a>
<FONT color="green">343</FONT>         *     &lt;li&gt;the weights array contains one or more infinite values&lt;/li&gt;<a name="line.343"></a>
<FONT color="green">344</FONT>         *     &lt;li&gt;the weights array contains one or more NaN values&lt;/li&gt;<a name="line.344"></a>
<FONT color="green">345</FONT>         *     &lt;li&gt;the weights array contains negative values&lt;/li&gt;<a name="line.345"></a>
<FONT color="green">346</FONT>         * &lt;/ul&gt;&lt;/p&gt;<a name="line.346"></a>
<FONT color="green">347</FONT>         * &lt;p&gt;<a name="line.347"></a>
<FONT color="green">348</FONT>         * Does not change the internal state of the statistic.&lt;/p&gt;<a name="line.348"></a>
<FONT color="green">349</FONT>         * &lt;p&gt;<a name="line.349"></a>
<FONT color="green">350</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if either array is null.&lt;/p&gt;<a name="line.350"></a>
<FONT color="green">351</FONT>         *<a name="line.351"></a>
<FONT color="green">352</FONT>         * @param values the input array<a name="line.352"></a>
<FONT color="green">353</FONT>         * @param weights the weights array<a name="line.353"></a>
<FONT color="green">354</FONT>         * @return the weighted variance of the values<a name="line.354"></a>
<FONT color="green">355</FONT>         * @throws IllegalArgumentException if the parameters are not valid<a name="line.355"></a>
<FONT color="green">356</FONT>         * @since 2.1<a name="line.356"></a>
<FONT color="green">357</FONT>         */<a name="line.357"></a>
<FONT color="green">358</FONT>        public double evaluate(final double[] values, final double[] weights) {<a name="line.358"></a>
<FONT color="green">359</FONT>            return evaluate(values, weights, 0, values.length);<a name="line.359"></a>
<FONT color="green">360</FONT>        }<a name="line.360"></a>
<FONT color="green">361</FONT>    <a name="line.361"></a>
<FONT color="green">362</FONT>        /**<a name="line.362"></a>
<FONT color="green">363</FONT>         * Returns the variance of the entries in the specified portion of<a name="line.363"></a>
<FONT color="green">364</FONT>         * the input array, using the precomputed mean value.  Returns<a name="line.364"></a>
<FONT color="green">365</FONT>         * &lt;code&gt;Double.NaN&lt;/code&gt; if the designated subarray is empty.<a name="line.365"></a>
<FONT color="green">366</FONT>         * &lt;p&gt;<a name="line.366"></a>
<FONT color="green">367</FONT>         * See {@link Variance} for details on the computing algorithm.&lt;/p&gt;<a name="line.367"></a>
<FONT color="green">368</FONT>         * &lt;p&gt;<a name="line.368"></a>
<FONT color="green">369</FONT>         * The formula used assumes that the supplied mean value is the arithmetic<a name="line.369"></a>
<FONT color="green">370</FONT>         * mean of the sample data, not a known population parameter.  This method<a name="line.370"></a>
<FONT color="green">371</FONT>         * is supplied only to save computation when the mean has already been<a name="line.371"></a>
<FONT color="green">372</FONT>         * computed.&lt;/p&gt;<a name="line.372"></a>
<FONT color="green">373</FONT>         * &lt;p&gt;<a name="line.373"></a>
<FONT color="green">374</FONT>         * Returns 0 for a single-value (i.e. length = 1) sample.&lt;/p&gt;<a name="line.374"></a>
<FONT color="green">375</FONT>         * &lt;p&gt;<a name="line.375"></a>
<FONT color="green">376</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if the array is null.&lt;/p&gt;<a name="line.376"></a>
<FONT color="green">377</FONT>         * &lt;p&gt;<a name="line.377"></a>
<FONT color="green">378</FONT>         * Does not change the internal state of the statistic.&lt;/p&gt;<a name="line.378"></a>
<FONT color="green">379</FONT>         *<a name="line.379"></a>
<FONT color="green">380</FONT>         * @param values the input array<a name="line.380"></a>
<FONT color="green">381</FONT>         * @param mean the precomputed mean value<a name="line.381"></a>
<FONT color="green">382</FONT>         * @param begin index of the first array element to include<a name="line.382"></a>
<FONT color="green">383</FONT>         * @param length the number of elements to include<a name="line.383"></a>
<FONT color="green">384</FONT>         * @return the variance of the values or Double.NaN if length = 0<a name="line.384"></a>
<FONT color="green">385</FONT>         * @throws IllegalArgumentException if the array is null or the array index<a name="line.385"></a>
<FONT color="green">386</FONT>         *  parameters are not valid<a name="line.386"></a>
<FONT color="green">387</FONT>         */<a name="line.387"></a>
<FONT color="green">388</FONT>        public double evaluate(final double[] values, final double mean,<a name="line.388"></a>
<FONT color="green">389</FONT>                final int begin, final int length) {<a name="line.389"></a>
<FONT color="green">390</FONT>    <a name="line.390"></a>
<FONT color="green">391</FONT>            double var = Double.NaN;<a name="line.391"></a>
<FONT color="green">392</FONT>    <a name="line.392"></a>
<FONT color="green">393</FONT>            if (test(values, begin, length)) {<a name="line.393"></a>
<FONT color="green">394</FONT>                if (length == 1) {<a name="line.394"></a>
<FONT color="green">395</FONT>                    var = 0.0;<a name="line.395"></a>
<FONT color="green">396</FONT>                } else if (length &gt; 1) {<a name="line.396"></a>
<FONT color="green">397</FONT>                    double accum = 0.0;<a name="line.397"></a>
<FONT color="green">398</FONT>                    double dev = 0.0;<a name="line.398"></a>
<FONT color="green">399</FONT>                    double accum2 = 0.0;<a name="line.399"></a>
<FONT color="green">400</FONT>                    for (int i = begin; i &lt; begin + length; i++) {<a name="line.400"></a>
<FONT color="green">401</FONT>                        dev = values[i] - mean;<a name="line.401"></a>
<FONT color="green">402</FONT>                        accum += dev * dev;<a name="line.402"></a>
<FONT color="green">403</FONT>                        accum2 += dev;<a name="line.403"></a>
<FONT color="green">404</FONT>                    }<a name="line.404"></a>
<FONT color="green">405</FONT>                    double len = length;<a name="line.405"></a>
<FONT color="green">406</FONT>                    if (isBiasCorrected) {<a name="line.406"></a>
<FONT color="green">407</FONT>                        var = (accum - (accum2 * accum2 / len)) / (len - 1.0);<a name="line.407"></a>
<FONT color="green">408</FONT>                    } else {<a name="line.408"></a>
<FONT color="green">409</FONT>                        var = (accum - (accum2 * accum2 / len)) / len;<a name="line.409"></a>
<FONT color="green">410</FONT>                    }<a name="line.410"></a>
<FONT color="green">411</FONT>                }<a name="line.411"></a>
<FONT color="green">412</FONT>            }<a name="line.412"></a>
<FONT color="green">413</FONT>            return var;<a name="line.413"></a>
<FONT color="green">414</FONT>        }<a name="line.414"></a>
<FONT color="green">415</FONT>    <a name="line.415"></a>
<FONT color="green">416</FONT>        /**<a name="line.416"></a>
<FONT color="green">417</FONT>         * Returns the variance of the entries in the input array, using the<a name="line.417"></a>
<FONT color="green">418</FONT>         * precomputed mean value.  Returns &lt;code&gt;Double.NaN&lt;/code&gt; if the array<a name="line.418"></a>
<FONT color="green">419</FONT>         * is empty.<a name="line.419"></a>
<FONT color="green">420</FONT>         * &lt;p&gt;<a name="line.420"></a>
<FONT color="green">421</FONT>         * See {@link Variance} for details on the computing algorithm.&lt;/p&gt;<a name="line.421"></a>
<FONT color="green">422</FONT>         * &lt;p&gt;<a name="line.422"></a>
<FONT color="green">423</FONT>         * If &lt;code&gt;isBiasCorrected&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt; the formula used<a name="line.423"></a>
<FONT color="green">424</FONT>         * assumes that the supplied mean value is the arithmetic mean of the<a name="line.424"></a>
<FONT color="green">425</FONT>         * sample data, not a known population parameter.  If the mean is a known<a name="line.425"></a>
<FONT color="green">426</FONT>         * population parameter, or if the "population" version of the variance is<a name="line.426"></a>
<FONT color="green">427</FONT>         * desired, set &lt;code&gt;isBiasCorrected&lt;/code&gt; to &lt;code&gt;false&lt;/code&gt; before<a name="line.427"></a>
<FONT color="green">428</FONT>         * invoking this method.&lt;/p&gt;<a name="line.428"></a>
<FONT color="green">429</FONT>         * &lt;p&gt;<a name="line.429"></a>
<FONT color="green">430</FONT>         * Returns 0 for a single-value (i.e. length = 1) sample.&lt;/p&gt;<a name="line.430"></a>
<FONT color="green">431</FONT>         * &lt;p&gt;<a name="line.431"></a>
<FONT color="green">432</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if the array is null.&lt;/p&gt;<a name="line.432"></a>
<FONT color="green">433</FONT>         * &lt;p&gt;<a name="line.433"></a>
<FONT color="green">434</FONT>         * Does not change the internal state of the statistic.&lt;/p&gt;<a name="line.434"></a>
<FONT color="green">435</FONT>         *<a name="line.435"></a>
<FONT color="green">436</FONT>         * @param values the input array<a name="line.436"></a>
<FONT color="green">437</FONT>         * @param mean the precomputed mean value<a name="line.437"></a>
<FONT color="green">438</FONT>         * @return the variance of the values or Double.NaN if the array is empty<a name="line.438"></a>
<FONT color="green">439</FONT>         * @throws IllegalArgumentException if the array is null<a name="line.439"></a>
<FONT color="green">440</FONT>         */<a name="line.440"></a>
<FONT color="green">441</FONT>        public double evaluate(final double[] values, final double mean) {<a name="line.441"></a>
<FONT color="green">442</FONT>            return evaluate(values, mean, 0, values.length);<a name="line.442"></a>
<FONT color="green">443</FONT>        }<a name="line.443"></a>
<FONT color="green">444</FONT>    <a name="line.444"></a>
<FONT color="green">445</FONT>        /**<a name="line.445"></a>
<FONT color="green">446</FONT>         * Returns the weighted variance of the entries in the specified portion of<a name="line.446"></a>
<FONT color="green">447</FONT>         * the input array, using the precomputed weighted mean value.  Returns<a name="line.447"></a>
<FONT color="green">448</FONT>         * &lt;code&gt;Double.NaN&lt;/code&gt; if the designated subarray is empty.<a name="line.448"></a>
<FONT color="green">449</FONT>         * &lt;p&gt;<a name="line.449"></a>
<FONT color="green">450</FONT>         * Uses the formula &lt;pre&gt;<a name="line.450"></a>
<FONT color="green">451</FONT>         *   &amp;Sigma;(weights[i]*(values[i] - mean)&lt;sup&gt;2&lt;/sup&gt;)/(&amp;Sigma;(weights[i]) - 1)<a name="line.451"></a>
<FONT color="green">452</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.452"></a>
<FONT color="green">453</FONT>         * &lt;p&gt;<a name="line.453"></a>
<FONT color="green">454</FONT>         * The formula used assumes that the supplied mean value is the weighted arithmetic<a name="line.454"></a>
<FONT color="green">455</FONT>         * mean of the sample data, not a known population parameter. This method<a name="line.455"></a>
<FONT color="green">456</FONT>         * is supplied only to save computation when the mean has already been<a name="line.456"></a>
<FONT color="green">457</FONT>         * computed.&lt;/p&gt;<a name="line.457"></a>
<FONT color="green">458</FONT>         * &lt;p&gt;<a name="line.458"></a>
<FONT color="green">459</FONT>         * This formula will not return the same result as the unweighted variance when all<a name="line.459"></a>
<FONT color="green">460</FONT>         * weights are equal, unless all weights are equal to 1. The formula assumes that<a name="line.460"></a>
<FONT color="green">461</FONT>         * weights are to be treated as "expansion values," as will be the case if for example<a name="line.461"></a>
<FONT color="green">462</FONT>         * the weights represent frequency counts. To normalize weights so that the denominator<a name="line.462"></a>
<FONT color="green">463</FONT>         * in the variance computation equals the length of the input vector minus one, use &lt;pre&gt;<a name="line.463"></a>
<FONT color="green">464</FONT>         *   &lt;code&gt;evaluate(values, MathUtils.normalizeArray(weights, values.length), mean); &lt;/code&gt;<a name="line.464"></a>
<FONT color="green">465</FONT>         * &lt;/pre&gt;<a name="line.465"></a>
<FONT color="green">466</FONT>         * &lt;p&gt;<a name="line.466"></a>
<FONT color="green">467</FONT>         * Returns 0 for a single-value (i.e. length = 1) sample.&lt;/p&gt;<a name="line.467"></a>
<FONT color="green">468</FONT>         * &lt;p&gt;<a name="line.468"></a>
<FONT color="green">469</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if any of the following are true:<a name="line.469"></a>
<FONT color="green">470</FONT>         * &lt;ul&gt;&lt;li&gt;the values array is null&lt;/li&gt;<a name="line.470"></a>
<FONT color="green">471</FONT>         *     &lt;li&gt;the weights array is null&lt;/li&gt;<a name="line.471"></a>
<FONT color="green">472</FONT>         *     &lt;li&gt;the weights array does not have the same length as the values array&lt;/li&gt;<a name="line.472"></a>
<FONT color="green">473</FONT>         *     &lt;li&gt;the weights array contains one or more infinite values&lt;/li&gt;<a name="line.473"></a>
<FONT color="green">474</FONT>         *     &lt;li&gt;the weights array contains one or more NaN values&lt;/li&gt;<a name="line.474"></a>
<FONT color="green">475</FONT>         *     &lt;li&gt;the weights array contains negative values&lt;/li&gt;<a name="line.475"></a>
<FONT color="green">476</FONT>         *     &lt;li&gt;the start and length arguments do not determine a valid array&lt;/li&gt;<a name="line.476"></a>
<FONT color="green">477</FONT>         * &lt;/ul&gt;&lt;/p&gt;<a name="line.477"></a>
<FONT color="green">478</FONT>         * &lt;p&gt;<a name="line.478"></a>
<FONT color="green">479</FONT>         * Does not change the internal state of the statistic.&lt;/p&gt;<a name="line.479"></a>
<FONT color="green">480</FONT>         *<a name="line.480"></a>
<FONT color="green">481</FONT>         * @param values the input array<a name="line.481"></a>
<FONT color="green">482</FONT>         * @param weights the weights array<a name="line.482"></a>
<FONT color="green">483</FONT>         * @param mean the precomputed weighted mean value<a name="line.483"></a>
<FONT color="green">484</FONT>         * @param begin index of the first array element to include<a name="line.484"></a>
<FONT color="green">485</FONT>         * @param length the number of elements to include<a name="line.485"></a>
<FONT color="green">486</FONT>         * @return the variance of the values or Double.NaN if length = 0<a name="line.486"></a>
<FONT color="green">487</FONT>         * @throws IllegalArgumentException if the parameters are not valid<a name="line.487"></a>
<FONT color="green">488</FONT>         * @since 2.1<a name="line.488"></a>
<FONT color="green">489</FONT>         */<a name="line.489"></a>
<FONT color="green">490</FONT>        public double evaluate(final double[] values, final double[] weights,<a name="line.490"></a>
<FONT color="green">491</FONT>                               final double mean, final int begin, final int length) {<a name="line.491"></a>
<FONT color="green">492</FONT>    <a name="line.492"></a>
<FONT color="green">493</FONT>            double var = Double.NaN;<a name="line.493"></a>
<FONT color="green">494</FONT>    <a name="line.494"></a>
<FONT color="green">495</FONT>            if (test(values, weights, begin, length)) {<a name="line.495"></a>
<FONT color="green">496</FONT>                if (length == 1) {<a name="line.496"></a>
<FONT color="green">497</FONT>                    var = 0.0;<a name="line.497"></a>
<FONT color="green">498</FONT>                } else if (length &gt; 1) {<a name="line.498"></a>
<FONT color="green">499</FONT>                    double accum = 0.0;<a name="line.499"></a>
<FONT color="green">500</FONT>                    double dev = 0.0;<a name="line.500"></a>
<FONT color="green">501</FONT>                    double accum2 = 0.0;<a name="line.501"></a>
<FONT color="green">502</FONT>                    for (int i = begin; i &lt; begin + length; i++) {<a name="line.502"></a>
<FONT color="green">503</FONT>                        dev = values[i] - mean;<a name="line.503"></a>
<FONT color="green">504</FONT>                        accum += weights[i] * (dev * dev);<a name="line.504"></a>
<FONT color="green">505</FONT>                        accum2 += weights[i] * dev;<a name="line.505"></a>
<FONT color="green">506</FONT>                    }<a name="line.506"></a>
<FONT color="green">507</FONT>    <a name="line.507"></a>
<FONT color="green">508</FONT>                    double sumWts = 0;<a name="line.508"></a>
<FONT color="green">509</FONT>                    for (int i = 0; i &lt; weights.length; i++) {<a name="line.509"></a>
<FONT color="green">510</FONT>                        sumWts += weights[i];<a name="line.510"></a>
<FONT color="green">511</FONT>                    }<a name="line.511"></a>
<FONT color="green">512</FONT>    <a name="line.512"></a>
<FONT color="green">513</FONT>                    if (isBiasCorrected) {<a name="line.513"></a>
<FONT color="green">514</FONT>                        var = (accum - (accum2 * accum2 / sumWts)) / (sumWts - 1.0);<a name="line.514"></a>
<FONT color="green">515</FONT>                    } else {<a name="line.515"></a>
<FONT color="green">516</FONT>                        var = (accum - (accum2 * accum2 / sumWts)) / sumWts;<a name="line.516"></a>
<FONT color="green">517</FONT>                    }<a name="line.517"></a>
<FONT color="green">518</FONT>                }<a name="line.518"></a>
<FONT color="green">519</FONT>            }<a name="line.519"></a>
<FONT color="green">520</FONT>            return var;<a name="line.520"></a>
<FONT color="green">521</FONT>        }<a name="line.521"></a>
<FONT color="green">522</FONT>    <a name="line.522"></a>
<FONT color="green">523</FONT>        /**<a name="line.523"></a>
<FONT color="green">524</FONT>         * &lt;p&gt;Returns the weighted variance of the values in the input array, using<a name="line.524"></a>
<FONT color="green">525</FONT>         * the precomputed weighted mean value.&lt;/p&gt;<a name="line.525"></a>
<FONT color="green">526</FONT>         * &lt;p&gt;<a name="line.526"></a>
<FONT color="green">527</FONT>         * Uses the formula &lt;pre&gt;<a name="line.527"></a>
<FONT color="green">528</FONT>         *   &amp;Sigma;(weights[i]*(values[i] - mean)&lt;sup&gt;2&lt;/sup&gt;)/(&amp;Sigma;(weights[i]) - 1)<a name="line.528"></a>
<FONT color="green">529</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.529"></a>
<FONT color="green">530</FONT>         * &lt;p&gt;<a name="line.530"></a>
<FONT color="green">531</FONT>         * The formula used assumes that the supplied mean value is the weighted arithmetic<a name="line.531"></a>
<FONT color="green">532</FONT>         * mean of the sample data, not a known population parameter. This method<a name="line.532"></a>
<FONT color="green">533</FONT>         * is supplied only to save computation when the mean has already been<a name="line.533"></a>
<FONT color="green">534</FONT>         * computed.&lt;/p&gt;<a name="line.534"></a>
<FONT color="green">535</FONT>         * &lt;p&gt;<a name="line.535"></a>
<FONT color="green">536</FONT>         * This formula will not return the same result as the unweighted variance when all<a name="line.536"></a>
<FONT color="green">537</FONT>         * weights are equal, unless all weights are equal to 1. The formula assumes that<a name="line.537"></a>
<FONT color="green">538</FONT>         * weights are to be treated as "expansion values," as will be the case if for example<a name="line.538"></a>
<FONT color="green">539</FONT>         * the weights represent frequency counts. To normalize weights so that the denominator<a name="line.539"></a>
<FONT color="green">540</FONT>         * in the variance computation equals the length of the input vector minus one, use &lt;pre&gt;<a name="line.540"></a>
<FONT color="green">541</FONT>         *   &lt;code&gt;evaluate(values, MathUtils.normalizeArray(weights, values.length), mean); &lt;/code&gt;<a name="line.541"></a>
<FONT color="green">542</FONT>         * &lt;/pre&gt;<a name="line.542"></a>
<FONT color="green">543</FONT>         * &lt;p&gt;<a name="line.543"></a>
<FONT color="green">544</FONT>         * Returns 0 for a single-value (i.e. length = 1) sample.&lt;/p&gt;<a name="line.544"></a>
<FONT color="green">545</FONT>         * &lt;p&gt;<a name="line.545"></a>
<FONT color="green">546</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if any of the following are true:<a name="line.546"></a>
<FONT color="green">547</FONT>         * &lt;ul&gt;&lt;li&gt;the values array is null&lt;/li&gt;<a name="line.547"></a>
<FONT color="green">548</FONT>         *     &lt;li&gt;the weights array is null&lt;/li&gt;<a name="line.548"></a>
<FONT color="green">549</FONT>         *     &lt;li&gt;the weights array does not have the same length as the values array&lt;/li&gt;<a name="line.549"></a>
<FONT color="green">550</FONT>         *     &lt;li&gt;the weights array contains one or more infinite values&lt;/li&gt;<a name="line.550"></a>
<FONT color="green">551</FONT>         *     &lt;li&gt;the weights array contains one or more NaN values&lt;/li&gt;<a name="line.551"></a>
<FONT color="green">552</FONT>         *     &lt;li&gt;the weights array contains negative values&lt;/li&gt;<a name="line.552"></a>
<FONT color="green">553</FONT>         * &lt;/ul&gt;&lt;/p&gt;<a name="line.553"></a>
<FONT color="green">554</FONT>         * &lt;p&gt;<a name="line.554"></a>
<FONT color="green">555</FONT>         * Does not change the internal state of the statistic.&lt;/p&gt;<a name="line.555"></a>
<FONT color="green">556</FONT>         *<a name="line.556"></a>
<FONT color="green">557</FONT>         * @param values the input array<a name="line.557"></a>
<FONT color="green">558</FONT>         * @param weights the weights array<a name="line.558"></a>
<FONT color="green">559</FONT>         * @param mean the precomputed weighted mean value<a name="line.559"></a>
<FONT color="green">560</FONT>         * @return the variance of the values or Double.NaN if length = 0<a name="line.560"></a>
<FONT color="green">561</FONT>         * @throws IllegalArgumentException if the parameters are not valid<a name="line.561"></a>
<FONT color="green">562</FONT>         * @since 2.1<a name="line.562"></a>
<FONT color="green">563</FONT>         */<a name="line.563"></a>
<FONT color="green">564</FONT>        public double evaluate(final double[] values, final double[] weights, final double mean) {<a name="line.564"></a>
<FONT color="green">565</FONT>            return evaluate(values, weights, mean, 0, values.length);<a name="line.565"></a>
<FONT color="green">566</FONT>        }<a name="line.566"></a>
<FONT color="green">567</FONT>    <a name="line.567"></a>
<FONT color="green">568</FONT>        /**<a name="line.568"></a>
<FONT color="green">569</FONT>         * @return Returns the isBiasCorrected.<a name="line.569"></a>
<FONT color="green">570</FONT>         */<a name="line.570"></a>
<FONT color="green">571</FONT>        public boolean isBiasCorrected() {<a name="line.571"></a>
<FONT color="green">572</FONT>            return isBiasCorrected;<a name="line.572"></a>
<FONT color="green">573</FONT>        }<a name="line.573"></a>
<FONT color="green">574</FONT>    <a name="line.574"></a>
<FONT color="green">575</FONT>        /**<a name="line.575"></a>
<FONT color="green">576</FONT>         * @param biasCorrected The isBiasCorrected to set.<a name="line.576"></a>
<FONT color="green">577</FONT>         */<a name="line.577"></a>
<FONT color="green">578</FONT>        public void setBiasCorrected(boolean biasCorrected) {<a name="line.578"></a>
<FONT color="green">579</FONT>            this.isBiasCorrected = biasCorrected;<a name="line.579"></a>
<FONT color="green">580</FONT>        }<a name="line.580"></a>
<FONT color="green">581</FONT>    <a name="line.581"></a>
<FONT color="green">582</FONT>        /**<a name="line.582"></a>
<FONT color="green">583</FONT>         * {@inheritDoc}<a name="line.583"></a>
<FONT color="green">584</FONT>         */<a name="line.584"></a>
<FONT color="green">585</FONT>        @Override<a name="line.585"></a>
<FONT color="green">586</FONT>        public Variance copy() {<a name="line.586"></a>
<FONT color="green">587</FONT>            Variance result = new Variance();<a name="line.587"></a>
<FONT color="green">588</FONT>            copy(this, result);<a name="line.588"></a>
<FONT color="green">589</FONT>            return result;<a name="line.589"></a>
<FONT color="green">590</FONT>        }<a name="line.590"></a>
<FONT color="green">591</FONT>    <a name="line.591"></a>
<FONT color="green">592</FONT>        /**<a name="line.592"></a>
<FONT color="green">593</FONT>         * Copies source to dest.<a name="line.593"></a>
<FONT color="green">594</FONT>         * &lt;p&gt;Neither source nor dest can be null.&lt;/p&gt;<a name="line.594"></a>
<FONT color="green">595</FONT>         *<a name="line.595"></a>
<FONT color="green">596</FONT>         * @param source Variance to copy<a name="line.596"></a>
<FONT color="green">597</FONT>         * @param dest Variance to copy to<a name="line.597"></a>
<FONT color="green">598</FONT>         * @throws NullPointerException if either source or dest is null<a name="line.598"></a>
<FONT color="green">599</FONT>         */<a name="line.599"></a>
<FONT color="green">600</FONT>        public static void copy(Variance source, Variance dest) {<a name="line.600"></a>
<FONT color="green">601</FONT>            if (source == null ||<a name="line.601"></a>
<FONT color="green">602</FONT>                dest == null) {<a name="line.602"></a>
<FONT color="green">603</FONT>                throw new NullArgumentException();<a name="line.603"></a>
<FONT color="green">604</FONT>            }<a name="line.604"></a>
<FONT color="green">605</FONT>            dest.setData(source.getDataRef());<a name="line.605"></a>
<FONT color="green">606</FONT>            dest.moment = source.moment.copy();<a name="line.606"></a>
<FONT color="green">607</FONT>            dest.isBiasCorrected = source.isBiasCorrected;<a name="line.607"></a>
<FONT color="green">608</FONT>            dest.incMoment = source.incMoment;<a name="line.608"></a>
<FONT color="green">609</FONT>        }<a name="line.609"></a>
<FONT color="green">610</FONT>    }<a name="line.610"></a>




























































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